2 Answers
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There are a few ways to remove curses from equipment other than the very obvious "Use the remove curse effect from scrolls or spellbooks".

If you have a potion of holy water, you can use that to bless it. Yes, it uses up your holy water, but that sacrifice will probably get you a lot further than the lost equipment slot and offense of having a pickaxe welded to your hand.

If you dip a cursed item into a fountain, the water may glow and uncurse the item. This isn't guaranteed, and you may rust the item in the process, but it's a simple way to handle that. This is an uncommon, but not rare, chance. Beware all the dangers of fountains, though.

An uncursed or better scroll of enchant weapon or scroll of enchant armor should uncurse offending equipment, if my memory is correct.

Prayer works, but the chance depends on the item. It's more successful when you've got both hands welded onto the same weapon than it is if you have only lost the utility of a single hand. But if you can afford the prayer, this is a simple way to get it done.

A magic trap has a chance of removing curses on your person. This is not a very good chance and can easily spell your demise early on, though.

If you have a wand of cancellation, then that will cancel a curse, as well as any enchantments on the item. If you plan to use it, consider dropping all the rest of your stuff so you don't cancel all of that.

You can also opt to get the item stolen. Nymphs can steal it from you, regardless of the status, so you can entice one to steal it right off of you.

Polymorph can also remove the item, if you turn into a form that doesn't have hands for example or otherwise cannot wield it. Or, if you're hungry, you could turn into a xorn or rust monster to just eat that metal pickaxe.